ROR question

[DSchles]

Thanks for your reply.

I found that the long term ROR will be much lower than the expected 13.53%(one kelly bankroll and betting) for game with relatively high ev(>10%) and high S.D(>4), this was confirmed by simulations and LONG TERM RISK CALCULATOR.

Here is a real game with ev = 9.46%, S.D = 3.685, BANKROLL = 144 units(one kelly bankroll),

1) ROR(long term risk calculator) = 12.85%
2) ROR(risk calculator with time constraint, 1000000 rounds) = 13.45%
3) ROR(my own simulations) = 12.01%

Question 1 : I thought long term ROR should be 13.53%(compare to 12.85%) ?
Question 2 : I thought trip ROR should be LOWER than long term ROR ? Why trip ROR is higher ?

Any comments ?

1. For (1), it would appear that the calculator uses the formula on p. 112 of BJA3. Personally, I have always used the first of the two formulas on the top of page 113 for the formula. It is what was used to create all the charts that follow in the chapter. If you use the values you provided in that formula for risk, you will get 13.53%.

2. Obviously, for (2), there really is no time time constraint at all, so the answer, 13.45%, should indeed, be virtually the same as that for (1), with no time constraint.

3. No criticism intended, but I have no idea what the standard error of your simulations may be, or if they were done correctly, so I really can't comment except to say that you should also read pp. 140-146 to realize that while the formulas are reasonably accurate approximations, they are NOT perfect.

Don

[James989]

1. For (1), it would appear that the calculator uses the formula on p. 112 of BJA3. Personally, I have always used the first of the two formulas on the top of page 113 for the formula. It is what was used to create all the charts that follow in the chapter. If you use the values you provided in that formula for risk, you will get 13.53%.

2. Obviously, for (2), there really is no time time constraint at all, so the answer, 13.45%, should indeed, be virtually the same as that for (1), with no time constraint.

3. No criticism intended, but I have no idea what the standard error of your simulations may be, or if they were done correctly, so I really can't comment except to say that you should also read pp. 140-146 to realize that while the formulas are reasonably accurate approximations, they are NOT perfect.

Don

Thanks Don, really appreciate your guidance and help.

Here are the rules of the above-mentioned game, there are 42 nos of balls( with label 1 to 42 ) in a box, player picks three numbers with total cost of $1, balls in box will be mixed "randomly" and 1 ball will be drawn from the box, if the draw number match any number of your pick, you will get pay $13.50( net win = 13.50 -1 = $12.50). However, from my few days observation, there are always 5( at least !) balls at certain corner of the box will never "mix" with other 37 balls !

Below is a simple program that how I model this game, could you(or any other experts) please help to find any mistakes or errors ?

42 Balls.jpg

[DSchles]

Thanks Don, really appreciate your guidance and help.

Here are the rules of the above-mentioned game, there are 42 nos of balls( with label 1 to 42 ) in a box, player picks three numbers with total cost of $1, balls in box will be mixed "randomly" and 1 ball will be drawn from the box, if the draw number match any number of your pick, you will get pay $13.50( net win = 13.50 -1 = $12.50). However, from my few days observation, there are always 5( at least !) balls at certain corner of the box will never "mix" with other 37 balls !

Below is a simple program that how I model this game, could you(or any other experts) please help to find any mistakes or errors ?

42 Balls.jpg

I can't help you with programming. The e.v. and s.d. are correct. Why don't you run more than a million rounds? What is the standard error your way? In any event, what's the difference if the ROR is 12% or 13%? Why should you care? Just play the game with more than 144 units and make a fortune.

Don

[James989]

That's true, there is no difference if the ROR is 12% or 13% in reality.

Thanks Don.